To extend a running distance and improve fuel consumption in a vehicle including a connecting/disconnecting device (e.g., a clutch) separating an engine and wheels and a transmission transmitting the power of the engine toward the wheels, it is conceivable that the vehicle is allowed to perform an inertia running mode when a predetermined condition is satisfied during a normal running mode performed by the power of the engine while the engine and the wheels are coupled. For example, in Patent Document 1, a control device of a vehicle is proposed that releases a clutch during running of the vehicle to separate an engine and wheels for allowing the vehicle to perform the inertia running mode on the condition of accelerator-off etc. Patent Document 1 describes that a state of the engine during the inertia running mode is an “idle state” or a “stop state” without particular distinction. In Patent Document 1, conditions for canceling such an inertia running mode (i.e., conditions for returning to a normal running mode) are exemplified as accelerator-on, brake-on, steering of a predetermined steering angle or more, a shift lever operation, an inter-vehicle distance of a predetermined value or less, a reduction in vehicle speed, an increase in vehicle speed on a descending road, etc.